10/29/2008, 04:49 AM
(This post was last modified: 11/23/2008, 01:00 AM by Kouznetsov.)
Hello, I did not find figuires of power of exponential. So, I suggest few for
levels
and
are shown with thick lines in the comples
for values
One of levels
Also, levels
which is fixed point of logarithm.
The thick pink lines indicate the cuts of the complex plane.
Graphics are symmetric with respect to the real axis; at real
Below I incert the graphic
...
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After to post the pics, I got the crytics (see the first comment). bo198214 suggests that I describe the method. I expected, that the method is obvious from the name of the forum...
where
The entire soluiton of this equation is described by Kneser [1]; he used it to construct
I have implemented tetration "tet", id est, the function
My tetation [2] is holomorphic in the whole complex
In order to understand, how does the inverse function work, I plot the image of the upper halfplane with function kslog.
Images of gridlines
References:
1. H.Kneser. Reelle analytische Losungen der Gleichung
2. D.Kouznetsov. Solution of
Mathematics Of Computations, in press. The up-to-last version is available at my homepage http://www.ils.uec.ac.jp/~dima/PAPERS/analuxp99.pdf
3. http://en.citizendium.org/wiki/Tetration